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Kei-Ichi Kondo

Publications and source records attributed to Kei-Ichi Kondo.

At least 109 records · Page 6Linked to original sources
arXiv2008

Magnetic Monopole Loops supported by a Meron pair as the Quark Confiner

We give an analytical solution representing circular magnetic monopole loops joining a pair of merons in the four-dimensional Euclidean SU(2) Yang-Mills theory. This is achieved by solving the differential equation for the adjoint color (magnetic monopole) field in the two--meron background field within the recently developed reformulation of the Yang-Mills theory. Our analytical solution corresponds to the numerical solution found by Montero and Negele on a lattice. This result strongly suggests that a meron pair is the most relevant quark confiner in the original Yang-Mills theory, as Callan, Dashen and Gross suggested long ago.

hep-th↗
arXiv2008

Reformulating SU(N) Yang-Mills theory based on change of variables

We propose a new version of SU(N) Yang-Mills theory reformulated in terms of new field variables which are obtained by a nonlinear change of variables from the original Yang-Mills gauge field. The reformulated Yang-Mills theory enables us to study the low-energy dynamics by explicitly extracting the topological degrees of freedom such as magnetic monopoles and vortices to clarify the mechanism for quark confinement. The dual superconductivity in Yang-Mills theory is understood in a gauge-invariant manner, as demonstrated recently by a non-Abelian Stokes theorem for the Wilson loop operator, although the basic idea of this reformulation is based on the Cho-Faddeev-Niemi decomposition of the gauge potential.

hep-th↗
arXiv2008

Magnetic monopoles and center vortices as gauge-invariant topological defects simultaneously responsible for confinement

We give a gauge-invariant definition of the vortex surface in SU(N) Yang-Mills theory without using the gauge fixing procedure. In this construction, gauge-invariant magnetic monopoles with fractional magnetic charges emerge in the boundary of the non-oriented vortex surface such that the asymptotic string tension reproduces the correct $N$-ality dependence. We show that gauge-invariant magnetic monopoles and vortices are simultaneously responsible for quark confinement in four dimensional spacetime based on the Wilson criterion. These results are extracted from a non-Abelian Stokes theorem derived in the previous paper.

hep-th↗
arXiv2008

Wilson loop and magnetic monopole through a non-Abelian Stokes theorem

We show that the Wilson loop operator for SU(N) Yang-Mills gauge connection is exactly rewritten in terms of conserved gauge-invariant magnetic and electric currents through a non-Abelian Stokes theorem of the Diakonov-Petrov type. Here the magnetic current originates from the magnetic monopole derived in the gauge-invariant way from the pure Yang--Mills theory even in the absence of the Higgs scalar field, in sharp contrast to the 't Hooft-Polyakov magnetic monopole in the Georgi-Glashow gauge-Higgs model. The resulting representation indicates that the Wilson loop operator in fundamental representations can be a probe for a single magnetic monopole irrespective of $N$ in SU(N) Yang-Mills theory, against the conventional wisdom. Moreover, we show that the quantization condition for the magnetic charge follows from the fact that the non-Abelian Stokes theorem does not depend on the surface chosen for writing the surface integral. The obtained geometrical and topological representations of the Wilson loop operator have important implications to understanding quark confinement according to the dual superconductor picture.

hep-th↗
arXiv2008

Proving Abelian dominance in the Wilson loop operator

We give a gauge-independent definition of Abelian dominance in the Wilson loop operator and a constructive proof of the Abelian dominance through a non-Abelian Stokes theorem via lattice regularization. We obtain a necessary and sufficient condition for the Abelian dominance in the Wilson loop operator in the fundamental representation. In the continuum limit, the gauge field is decomposed such that the Abelian dominance is given as an exact operator relation, leading to the exact (100%) Abelian dominance. On a lattice, we estimate the deviation from the exact Abelian dominance due to non-zero lattice spacing. In order to obtain the best Abelian dominance on a lattice by minimizing the deviation, we discuss how to decompose the gauge field variable into the dominant part and the remaining one to be decoupled on a lattice.

hep-th↗
arXiv2006

Gauge-invariant gluon mass, infrared Abelian dominance and stability of magnetic vacuum

We give an argument for deriving analytically the infrared ``Abelian'' dominance in a gauge invariant way for the Wilson loop average in SU(2) Yang--Mills theory. In other words, we propose a possible mechanism for realizing the dynamical Abelian projection in the SU(2) gauge-invariant manner without breaking color symmetry. This supports validity of the dual superconductivity picture for quark confinement. We also discuss the stability of the vacuum with magnetic condensation as a by-product of this result.

hep-th↗
arXiv2006

Glueball mass from quantized knot solitons and gauge-invariant gluon mass

We propose an approach which enables one to obtain simultaneously the glueball mass and the gluon mass in the gauge-invariant way to shed new light on the mass gap problem in Yang-Mills theory. First, we point out that the Faddeev (Skyrme--Faddeev-Niemi) model can be induced through the gauge-invariant vacuum condensate of mass dimension two from SU(2) Yang-Mills theory. Second, we obtain the glueball mass spectrum by performing the collective coordinate quantization of the topological knot soliton in the Faddeev model. Third, we demonstrate that a relationship between the glueball mass and the gluon mass is obtained, since the gauge-invariant gluon mass is also induced from the relevant vacuum condensate. Finally, we determine physical values of two parameters in the Faddeev model and give an estimate of the relevant vacuum condensation in Yang-Mills theory. Our results indicate that the Faddeev model can play the role of a low-energy effective theory of the quantum SU(2) Yang-Mills theory.

hep-th↗
arXiv2005

Understanding the U(1) problem through dyon configuration in the Abelian projection

We show that the magnetic monopole promoted to the dyon due to the vacuum angle $θ$ resolves the U(1) problem in the sense that the dyon obtained in this way gives a dominant contribution to the topological susceptibility. For this purpose, we derive an Abelian-projected effective gauge theory written in terms of Abelian degrees of freedom, which is obtained by integrating out all the off-diagonal degrees of freedom involved in the SU(2) Yang-Mills theory with the vacuum angle $θ$. We evaluate the topological susceptibility by estimating the classical part of the effective dyon action obtained by performing the duality transformation. The obtained result is consistent with the Veneziano--Witten formula.

hep-th↗
arXiv2004

Magnetic condensation, Abelian dominance and instability of Savvidy vacuum

We show that a certain type of color magnetic condensation originating from magnetic monopole configurations is sufficient to provide the mass for off-diagonal gluons in the SU(2) Yang-Mills theory under the Cho--Faddeev--Niemi decomposition. We point out that the generated gluon mass can cure the instability of the Savvidy vacuum. In fact, such a novel type of magnetic condensation is shown to occur by calculating the effective potential. This enables us to explain the infrared Abelian dominance and monopole dominance by way of a non-Abelian Stokes theorem, which suggests the dual superconductivity picture of quark confinement. Finally, we discuss the implication to the Faddeev-Skyrme model with knot soliton as a low-energy effective theory of Yang-Mills theory.

hep-th↗
arXiv2003

Non-perturbative propagators and dimension 2 condensate in Yang-Mills theory

We have found ultraviolet asymptotic slutions of the Schwinger-Dyson equation for the gluon and ghost propagators which have simultaneously the perturbative logarithmic correction and the non-perturbative $1/p^2$ power correction. By including the perturbative corrections, the power correction reproduces exactly the leading OPE result suggesting the existence of dimension two condensate.

hep-lat↗
arXiv2002

Consistent power corrections to ultraviolet asymptotic solutions in Yang-Mills theory

We show that the $1/p^2$ power corrections to the ultraviolet asymptotic solutions are allowed as consistent solutions of the coupled Schwinger-Dyson equation for the gluon and (Faddeev-Popov) ghost propagators in Yang-Mills theory. This result supports the existence of the vacuum condensate $ $ with mass dimension 2, as recently suggested by the operator product expansion and lattice simulations. We compare the solution with the result of operator product expansion.

hep-th↗
arXiv2002

Infrared and ultraviolet asymptotic solutions to gluon and ghost propagators in Yang-Mills theory

We examine the possibility that there may exist a logarithmic correction to the infrared asymptotic solution with power behavior which has recently been found for the gluon and Faddeev-Popov ghost propagators in the Landau gauge. We propose a new Ansatz to find a pair of solutions for the gluon and ghost form factors by solving the coupled Schwinger-Dyson equation under a simple truncation. This Ansatz enables us to derive the infrared and ultraviolet asymptotic solutions simultaneously and to understand why the power solution and the logarithmic solution is possible only in the infrared and ultraviolet limit respectively. Even in the presence of the logarithmic correction, the gluon propagator vanishes and the ghost propagator is enhanced in the infrared limit, and the gluon-ghost-antighost coupling constant has an infrared fixed point (but with a different $β$ function). This situation is consistent with Gribov-Zwanziger confinement scenario and color confinement criterion of Kugo and Ojima.

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